The quantum Kibble-Zurek mechanism predicts universal dynamical behavior in the vicinity of quantum phase transitions. While the mechanism is today well understood in one-dimensional systems, many questions in higher dimensions remain open. In our work [arXiv:2106.09046], we took the first steps towards exploring dynamical universality in two dimensions by numerical means. We studied the dynamical crossing of the QPT in the paradigmatic Ising model by a joint effort of state-of-the-art computational methods. In my presentation I will focus on the contribution of a new approach to simulate many-body quantum dynamics with neural quantum states.

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